Problem: Graph this system of equations and solve. $x+3y = 12$ $5x-3y = 6$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$ $\llap{-}2$ $\llap{-}3$ $\llap{-}4$ $\llap{-}5$ $\llap{-}6$ $\llap{-}7$ $\llap{-}8$ $\llap{-}9$ $\llap{-}10$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$ $\llap{-}2$ $\llap{-}3$ $\llap{-}4$ $\llap{-}5$ $\llap{-}6$ $\llap{-}7$ $\llap{-}8$ $\llap{-}9$ $\llap{-}10$ Click and drag the points to move the lines.
Solution: Convert the first equation, $x+3y = 12$ , to slope-intercept form. $y = -\dfrac{1}{3} x + 4$ The y-intercept for the first equation is $4$ , so the first line must pass through the point $(0, 4)$ The slope for the first equation is $-\dfrac{1}{3}$ . Remember that the slope tells you rise over run. So in this case for every $1$ position you move down (because it's negative) You must also move $3$ positions to the right. $3$ positions to the right. Graph the blue line so it passes through $(0, 4)$ and $(3, 3)$ Convert the second equation, $5x-3y = 6$ , to slope-intercept form. $y = \dfrac{5}{3} x - 2$ The y-intercept for the second equation is $-2$ , so the second line must pass through the point $(0, -2)$ The slope for the second equation is $\dfrac{5}{3}$ . Remember that the slope tells you rise over run. So in this case for every $5$ positions you move up You must also move $3$ positions to the right. $3$ positions to the right. $5$ positions up from $(0, -2)$ is $(3, 3)$ Graph the green line so it passes through $(0, -2)$ and $(3, 3)$ The solution is the point where the two lines intersect. The lines intersect at $(3, 3)$.